Combinatorics Seminar: Spherical special functions and symmetric polynomials

Event details Date: Monday, September 21, 2026 Time: 1:00 PM to 2:00 PM Location: Kaprielian Hall (KAP) - 414 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Elad Zelingher, USC Title: Spherical special functions and symmetric polynomials Abstract: In the representation theory of p-adic groups, an important class of representations are the spherical ones. These are representations that admit a spherical vector, that is, a non-zero vector that is invariant under a maximal compact open subgroup. It is known that for an irreducible spherical representation, its spherical vector is unique up to a scalar. Using this uniqueness, one can attach to the irreducible representation in question interesting functions. It is then desirable to find explicit formulas for these functions, which often turn out to essentially be some explicit symmetric polynomials in the representation data. In this talk I will give some classical examples of this phenomenon and talk about some new cases, some of which are still in progress. A crash course on p-adic numbers basics will be provided. Official event details: https://calendar.usc.edu/event/combinatorics-seminar-spherical-special-functions-and-symmetric-polynomials